If it's not a super long move I would just get four furniture dollys and put on under each corner. Run a strap around the dolly and shelter and roll it away.
I worked at a place that built modular homes and this is basically how we moved houses as they were being built. The dollys we used were made from multiple pieces of one inch thick plywood around 2 feet long and one foot wide and each had ten casters on it but the same principle works here. For that matter I helped move a car that had broken the ball joint with a movers dolly and it was a v8 ford crown vic.
I worked at a place that built modular homes and this is basically how we moved houses as they were being built. The dollys we used were made from multiple pieces of one inch thick plywood around 2 feet long and one foot wide and each had ten casters on it but the same principle works here. For that matter I helped move a car that had broken the ball joint with a movers dolly and it was a v8 ford crown vic.